7 The random variable \(X\) denotes the number of hours of cloud cover per day at a weather forecasting centre. The probability density function of \(X\) is given by $$f ( x ) = \begin{cases} \frac { ( x - 18 ) ^ { 2 } } { k } & 0 \leqslant x \leqslant 24
0 & \text { otherwise } \end{cases}$$ where \(k\) is a constant.

1. Show that \(k = 2016\).
2. On how many days in a year of 365 days can the centre expect to have less than 2 hours of cloud cover?
3. Find the mean number of hours of cloud cover per day.